Approximations of standard equivalence relations and Bernoulli percolation at pu

Damien Gaboriau; Robin Tucker-Drob

doi:10.1016/j.crma.2016.09.011

Dynamical systems/Probability theory

Approximations of standard equivalence relations and Bernoulli percolation at p_u
[Approximations de relations d'équivalence standard et percolation de Bernoulli à p_u]

Présenté par : Étienne Ghys

Damien Gaboriau ¹ ; Robin Tucker-Drob ²

¹ CNRS, Unité de mathématiques pures et appliquées, ENS-Lyon, Université de Lyon, France
² Department of Mathematics, Texas A&M University, College Station, TX, USA

Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1114-1118.

Résumé
Abstract

Le but de cette note est d'annoncer certains résultats d'équivalence orbitale, concernant notamment la notion d'approximation de relations d'équivalence standard préservant la mesure de probabilité par suites croissantes de sous-relations, avec application au comportement en $p_{u}$ de la percolation de Bernoulli sur les graphes de Cayley.

The goal of this note is to announce certain results in orbit equivalence theory, especially concerning the approximation of p.m.p. standard equivalence relations by increasing sequences of sub-relations, with application to the behavior of the Bernoulli percolation on Cayley graphs at the threshold $p_{u}$ .

Reçu le : 2015-07-06
Accepté le : 2016-09-27
Publié le : 2016-10-18

DOI : 10.1016/j.crma.2016.09.011

Affiliations des auteurs :

Damien Gaboriau ¹ ; Robin Tucker-Drob ²

¹ CNRS, Unité de mathématiques pures et appliquées, ENS-Lyon, Université de Lyon, France
² Department of Mathematics, Texas A&M University, College Station, TX, USA

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     author = {Damien Gaboriau and Robin Tucker-Drob},
     title = {Approximations of standard equivalence relations and {Bernoulli} percolation at \protect\emph{p}\protect\textsubscript{\protect\emph{u}}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1114--1118},
     publisher = {Elsevier},
     volume = {354},
     number = {11},
     year = {2016},
     doi = {10.1016/j.crma.2016.09.011},
     language = {en},
}

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Damien Gaboriau; Robin Tucker-Drob. Approximations of standard equivalence relations and Bernoulli percolation at p_u. Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1114-1118. doi : 10.1016/j.crma.2016.09.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.09.011/

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